Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We show that complete synchronization exists as an invariant solution, and give the necessary condition for it to be observed as a stable state. Moreover, in some relevant instances, such a necessary condition takes the form of a Master Stability Function. This generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture.

We address the problem of how the survival of cooperation in a social system depends on the motion of the individuals. Specifically, we study a model in which prisoner’s dilemma players are allowed to move in a two-dimensional plane. Our results show that cooperation can survive in such a system provided that both the temptation to defect and the velocity at which agents move are not too high. Moreover, we show that when these conditions are fulfilled, the only asymptotic state of the system is that in which all players are cooperators. Our results might have implications for the design of cooperative strategies in motion coordination and other applications including wireless networks.

Memristors are gaining increasing attention as next generation electronic devices. They are also becoming commonly used as fundamental blocks for building chaotic circuits, although often arbitrary (typically piece-wise linear or cubic) flux-charge characteristics are assumed. In this paper, a chaotic circuit based on the mathematical realistic model of the HP memristor is introduced. The circuit makes use of two HP memristors in antiparallel. Numerical results showing some of the chaotic attractors generated by this circuit and the behavior with respect to changes in its component values are described.

We study phase synchronization in a network motif with a starlike structure in which the central node's (the hub's) frequency is strongly detuned against the other peripheral nodes. We find numerically and experimentally a regime of remote synchronization (RS), where the peripheral nodes form a phase synchronized cluster, while the hub remains free with its own dynamics and serves just as a transmitter for the other nodes. We explain the mechanism for this RS by the existence of a free amplitude and also show that systems with a fixed or constant amplitude, such as the classic Kuramoto phase oscillator, are not able to generate this phenomenon. Further, we derive an analytic expression which supports our explanation of the mechanism.

We consider a set of mobile agents in a two dimensional space, each one of them carrying a chaotic oscillator, and discuss the related synchronization issues under the framework of time-variant networks. In particular, we show that, as far as the time scale for the motion of the agents is much shorter than that of the associated dynamical systems, the global behavior can be characterized by a scaled all-to-all Laplacian matrix, and the synchronization conditions depend on the agent density on the plane.

Chimera states, that is, dynamical regimes characterized by the existence of a symmetry-broken solution where a coherent domain and an incoherent one coexist, have been theoretically demonstrated and numerically found in networks of homogeneously coupled identical oscillators. In this work we experimentally investigate the behavior of a closed and an open chain of electronic circuits with neuron-like spiking dynamics and first neighbor connections. Experimental results show the onset of a regime that we call chimera states with quiescent and synchronous domains, where synchronization coexists with spatially patterned oscillation death. The whole experimental bifurcation scenario, showing how disordered states, synchronization, chimera states with quiescent and synchronous domains, and oscillatory death states emerge as coupling is varied, is presented.